Journal of Computational Finance

Risk.net

Exact pricing formulae for caps and swaptions in a Lévy term structure model

Ernst Eberlein and Wolfgang Kluge

ABSTRACT

We discuss the extension of the Lévy term structure model introduced in Eberlein and Raible (1999) to time-inhomogeneous Lévy processes. Time-inhomogeneity means that the increments of the driving process are independent but, in general, not stationary. Within this framework we derive analytical formulae for the prices of caps and floors using bilateral Laplace transforms. Under an additional assumption on the volatility structure we also derive an analytical formula for pricing swaptions. These formulae allow for a quick numerical evaluation and therefore for a calibration of the model to market data. An example of a model calibration based on prices of caps and swaptions is given.

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